{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a88166f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot  as plt\n",
    "\n",
    "from qiskit import(\n",
    "    QuantumCircuit, \n",
    "    ClassicalRegister, \n",
    "    QuantumRegister,\n",
    "    transpile)\n",
    "from qiskit.providers.basic_provider import BasicProvider\n",
    "\n",
    " \n",
    "backend = BasicProvider().get_backend('basic_simulator')\n",
    "\n",
    "\n",
    "from qiskit.quantum_info import SparsePauliOp\n",
    "from qiskit.circuit.library import efficient_su2, TwoLocal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "fa3f9555",
   "metadata": {},
   "outputs": [],
   "source": [
    "N_s = 8\n",
    "J = 0.4\n",
    "h = 1\n",
    "g = 0.3\n",
    "XX_terms = []\n",
    "Z_terms = []\n",
    "ZZ_terms = []\n",
    "for i in range(N_s):\n",
    "    term = list(\"I\" * N_s)\n",
    "    term[i] = \"X\"\n",
    "    term[(i + 1) % N_s] = \"X\"\n",
    "    XX_terms.append((\"\".join(term), -J))\n",
    "\n",
    "    term = list(\"I\" * N_s)\n",
    "    term[i] = \"Z\"\n",
    "    Z_terms.append((\"\".join(term), -h))\n",
    "\n",
    "    term = list(\"I\" * N_s)\n",
    "    term[i] = \"Z\"\n",
    "    term[(i + 1) % N_s] = \"Z\"\n",
    "    ZZ_terms.append((\"\".join(term), -g))\n",
    "\n",
    "Ham_terms = XX_terms + Z_terms + ZZ_terms\n",
    "\n",
    "Ham_op = SparsePauliOp.from_list(Ham_terms)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "570ad7f2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reference value: -10.64693\n"
     ]
    }
   ],
   "source": [
    "from qiskit_algorithms import NumPyMinimumEigensolver\n",
    "\n",
    "numpy_solver = NumPyMinimumEigensolver()\n",
    "result = numpy_solver.compute_minimum_eigenvalue(operator=Ham_op)\n",
    "ref_value = result._eigenvalue.real\n",
    "print(f\"Reference value: {ref_value:.5f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b5a40340",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1040x702.333 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# define ansatz and optimizer\n",
    "from qiskit.circuit.library import n_local\n",
    "from qiskit_algorithms.optimizers import SPSA, SLSQP\n",
    "iterations = 8000\n",
    "ansatzs = []\n",
    "for i in range(1):\n",
    "    ansatz = efficient_su2(N_s, reps=1, insert_barriers=False)\n",
    "    ansatzs.append(ansatz)\n",
    "spsa = SPSA(maxiter=iterations)\n",
    "# slsqp = SLSQP(maxiter=iterations)\n",
    "ansatzs[0].draw(\"mpl\", style=\"iqp\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5b594fc1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# define callback\n",
    "# note: Re-run this cell to restart lists before training\n",
    "counts = []\n",
    "values = []\n",
    "\n",
    "\n",
    "def store_intermediate_result(eval_count, parameters, mean, std):\n",
    "    counts.append(eval_count)\n",
    "    values.append(mean)\n",
    "# define Aer Estimator for noiseless statevector simulation\n",
    "from qiskit_algorithms.utils import algorithm_globals\n",
    "from qiskit_aer.primitives import EstimatorV2 as AerEstimator\n",
    "\n",
    "seed = 150\n",
    "algorithm_globals.random_seed = seed\n",
    "\n",
    "noiseless_estimator = AerEstimator(options={\"default_precision\": 1e-5})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c92d6477",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "VQE on Aer qasm simulator (no noise): -10.60404\n",
      "Delta from reference energy value is 0.04289\n"
     ]
    }
   ],
   "source": [
    "# instantiate and run VQE\n",
    "from qiskit_algorithms import VQE\n",
    "for i in range(len(ansatzs)):\n",
    "    # print(\"Layers: \", 3)\n",
    "    vqe = VQE(noiseless_estimator, ansatzs[i], optimizer=spsa, callback=store_intermediate_result)\n",
    "    result = vqe.compute_minimum_eigenvalue(operator=Ham_op)\n",
    "\n",
    "    print(f\"VQE on Aer qasm simulator (no noise): {result.eigenvalue.real:.5f}\")\n",
    "    print(f\"Delta from reference energy value is {(result.eigenvalue.real - ref_value):.5f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "72992360",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-5.92015997438642,\n",
       " 6.677033742376887,\n",
       " 2.7890706754166317,\n",
       " -3.4556226929655027,\n",
       " 2.758385190087413,\n",
       " 3.55297043325686,\n",
       " 3.5377656877783608,\n",
       " -3.5248419214878846,\n",
       " -0.3635217364531787,\n",
       " -0.377235236104753,\n",
       " 1.1689814421014677,\n",
       " 1.7222445386776386,\n",
       " 3.180300312107028,\n",
       " 6.226100428164154,\n",
       " -1.7270709586831672,\n",
       " 3.7284339764103827,\n",
       " 2.301539721769805,\n",
       " 2.9178346244897755,\n",
       " 5.734148750969991,\n",
       " 2.657350436053645,\n",
       " -0.13855393540934913,\n",
       " -2.555908615517727,\n",
       " 2.587214340900946,\n",
       " -3.394324035244324,\n",
       " -5.882624310600603,\n",
       " 6.02438504087176,\n",
       " -3.012775068224874,\n",
       " 0.01695823034398427,\n",
       " -6.304933277006159,\n",
       " 0.050630000599110256,\n",
       " 0.09849541016590174,\n",
       " 6.101619121699816,\n",
       " -3.476503907620536,\n",
       " 5.691900238554085,\n",
       " 5.213164263804339,\n",
       " -4.159571820744894,\n",
       " 3.0857553783632348,\n",
       " 0.03631948483341746,\n",
       " -3.1230099201814845,\n",
       " 4.525729319727423,\n",
       " -0.8048599542866909,\n",
       " 3.110901789850808,\n",
       " 2.926887796220247,\n",
       " -0.3105242973686296,\n",
       " 6.119143316912892,\n",
       " -5.891943695318574,\n",
       " 4.5692568014706065,\n",
       " -3.3102413064410428]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "thetas = []\n",
    "for key in result.optimal_parameters:\n",
    "    thetas.append(result.optimal_parameters[key])\n",
    "thetas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "5a6a269c",
   "metadata": {},
   "outputs": [],
   "source": [
    "file = 'vqe-thetas-N' + str(N_s)\n",
    "file += '-J' + str(J)\n",
    "file += '-h' + str(h)\n",
    "file += '-g' + str(g)\n",
    "file += '.npy'\n",
    "\n",
    "np.save(file, np.array(thetas))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "9020e7ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'vqe-thetas-N12-J1.0-h1-g0.2.npy'"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "a673a497",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Convergence with no noise')"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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www1KSUlRZmam3nvvPc2ePVudO3fW9ddfrzfffFO33nqrVqxYoT59+qikpESbN2/Wm2++qaVLl6pbt24VHue8887TzJkzFR4e7rlBYXR0tNq1a6f09HTPWFYkJSVFknTffffp2muvVWBgoC677DLPmwG1LTAwUI8++qhGjx6tvn376rrrrtPevXv11FNPKSEhQePGjauR40RFRWnKlCl68MEHNXDgQF1++eVKT0/X888/r+7du2v48OEn3Pamm25SZmamLrzwQrVo0UI7duzQM888oy5duniugpk4caLee+89XXrppRo1apRSUlKUn5+v9evX66233tL27dvVtGnTGjkXAEAt8dVjAwAAqGk//fSTGTNmjElISDB2u92EhYWZPn36mGeeecYcOXLE06+oqMg8+OCDpnXr1iYwMNDEx8ebKVOmePUx5uij7AYNGlTmOH379jV9+/Yt075lyxYjyUgyX375Zbk17t2719xxxx0mPj7eBAYGmtjYWNOvXz8zZ84cT5/Sx8ItXLiw3H0sWLDAJCUlGYfDYZKTk817771nBg8ebJKSksr0nTNnjklJSTHBwcEmLCzMdOzY0dxzzz1m9+7d1TrPgwcPmrFjx5rmzZsbu91uWrRoYUaOHOn1GMLCwkLz6KOPmrPOOss4HA4TGRlpUlJSzIMPPmiys7PLPadjffDBB0aSufjii73ab7rpJiPJzJ07t8w2Ou6RfcYcfdxc8+bNjdVq9Xp8nyRzxx13lNlHq1atzMiRIyus7URjs23bNiPJzJs3z6v9jTfeMF27djUOh8M0btzYDBs2zPz2228VHsOYPx7Z9+2335Z7/BUrVni1P/vssyYpKckEBgaamJgYc9ttt3k90tCYso/se+utt8xFF11koqOjjd1uNy1btjS33HKL2bNnj9d2ubm5ZsqUKaZt27bGbrebpk2bmt69e5snnnjCFBYWnvRcAAC+ZTGmhu84AwAA6lyXLl0UFRVV4ePXAABAw8Nn+gEAqEeKiorKfI76s88+07p163T++ef7pigAAHDaYqYfAIB6ZPv27erfv7+GDx+uuLg4bd68WbNnz1Z4eLg2bNigJk2a+LpEAABwGuFGfgAA1CORkZFKSUnR//3f/2n//v0KDQ3VoEGDNHPmTAI/AAAog5l+AAAAAAD8FJ/pBwAAAADATxH6AQAAAADwU3ymvwa43W7t3r1bYWFhslgsvi4HAAAAAODnjDHKzc1VXFycrNYTz+cT+mvA7t27FR8f7+syAAAAAAANzK+//qoWLVqccD2hvwaEhYVJOvrNdjqdPq4GAAAAAODvcnJyFB8f78mjJ0LorwGll/Q7nU5CPwAAAACgzpzsI+bcyA8AAAAAAD9F6AcAAAAAwE8R+gEAAAAA8FOEfgAAAAAA/BShHwAAAAAAP0XoBwAAAADATxH6AQAAAADwU4R+AAAAAAD8FKEfAAAAAAA/RehvYA7kufTT3lxflwEAAAAAqAMBvi4Adavb//tEkvTZ389XQtNQH1cDAAAAAKhNzPQ3UN//esjXJQAAAAAAahmhv4EyxtcVAAAAAABqG6G/gSL0AwAAAID/I/Q3UG5SPwAAAAD4PUJ/A1VUQugHAAAAAH9H6G9AzDGz+/f+b73XMgAAAADA/xD6G5AbX1njtfz08q0+qgQAAAAAUBf8MvQ/99xzSkhIUFBQkHr27KnVq1dX2H/hwoVKSkpSUFCQOnbsqA8//LCOKq1bn27e57X85PKffFQJAAAAAKAu+F3of+ONNzR+/HhNmzZN3333nTp37qwBAwZo37595fZftWqVrrvuOt144436/vvvdeWVV+rKK6/Uhg0b6rjyusfV/QAAAADg3yzGzz7Y3bNnT3Xv3l3PPvusJMntdis+Pl5/+9vfNHny5DL9hw4dqvz8fC1evNjTds4556hLly6aPXt2ucdwuVxyuVye5ZycHMXHxys7O1tOp7OGz6jmJEz+oEzb9pmDfFAJAAAAAOBU5OTkKDw8/KQ51K9m+gsLC7V27Vr179/f02a1WtW/f3+lpqaWu01qaqpXf0kaMGDACftL0owZMxQeHu55xcfH18wJ1KLsgiJflwAAAAAAqGN+FfoPHDigkpISxcTEeLXHxMQoIyOj3G0yMjKq1F+SpkyZouzsbM/r119/PfXia1mui9APAAAAAA1NgK8LqI8cDoccDoevy6iSAKtfvb8DAAAAAKgEv0qCTZs2lc1m0969e73a9+7dq9jY2HK3iY2NrVL/+orMDwAAAAANj19FQbvdrpSUFC1fvtzT5na7tXz5cvXq1avcbXr16uXVX5KWLVt2wv71lc1i8XUJAAAAAIA65neX948fP14jR45Ut27d1KNHDz355JPKz8/X6NGjJUkjRoxQ8+bNNWPGDEnSXXfdpb59++qf//ynBg0apAULFmjNmjWaM2eOL0+jxnF5PwAAAAA0PH4X+ocOHar9+/dr6tSpysjIUJcuXbRkyRLPzfp27twp6zEBuHfv3nr99dd1//33695779UZZ5yhd955R8nJyb46hVpB5gcAAACAhsdijDG+LqK+q+zzEX0p31Wss6YtLdO+bcYlsnDpPwAAAADUK5XNocz/NhDWEwR73vIBAAAAAP9F6G8gAm0nCP11XAcAAAAAoO4Q+huIAFv5Q82nOwAAAADAfxH6GzgiPwAAAAD4L0J/A8dEPwAAAAD4L0J/A2eY6wcAAAAAv0Xob+CY6QcAAAAA/0Xob0DeG9vH1yUAAAAAAOoQob8B6dQiokwbM/0AAAAA4L8I/Q3MxAHtvJb5TD8AAAAA+C9CfwNzxwVtvZaZ6QcAAAAA/0Xob4DaN3N6vibzAwAAAID/IvQ3QCN6tfJ8bZjqBwAAAAC/RehvgAKsFs/XRH4AAAAA8F+E/gbIajkm9JP6AQAAAMBvEfoboHaxYX8sEPoBAAAAwG8R+hugpGNCP4/sAwAAAAD/RehvgCxc3g8AAAAADQKhvwGyHPM1mR8AAAAA/BehvwE6ZqJfbqb6AQAAAMBvEfoboGMv7z9SVOLDSgAAAAAAtYnQ38At2ZDh6xIAAAAAALWE0N/AcXk/AAAAAPgvQn8D5ybzAwAAAIDfIvQ3cK99vcPXJQAAAAAAagmhv4H77dBhX5cAAAAAAKglhH4AAAAAAPyU34T+7du368Ybb1Tr1q0VHBysNm3aaNq0aSosLKxwu/PPP18Wi8Xrdeutt9ZR1QAAAAAA1J4AXxdQUzZv3iy3260XX3xRbdu21YYNGzRmzBjl5+friSeeqHDbMWPG6KGHHvIsh4SE1Ha5AAAAAADUOr8J/QMHDtTAgQM9y4mJiUpPT9cLL7xw0tAfEhKi2NjYSh/L5XLJ5XJ5lnNycqpeMAAAAAAAtcxvLu8vT3Z2tho3bnzSfvPnz1fTpk2VnJysKVOmqKCgoML+M2bMUHh4uOcVHx9fUyUDAAAAAFBj/Gam/3hbt27VM888c9JZ/r/+9a9q1aqV4uLi9MMPP2jSpElKT0/XokWLTrjNlClTNH78eM9yTk4OwR8AAAAAcNo57UP/5MmT9eijj1bYZ9OmTUpKSvIs79q1SwMHDtSQIUM0ZsyYCre9+eabPV937NhRzZo1U79+/fTzzz+rTZs25W7jcDjkcDiqcBYAAAAAANS90z70T5gwQaNGjaqwT2Jioufr3bt364ILLlDv3r01Z86cKh+vZ8+eko5eKXCi0A8AAAAAQH1w2of+qKgoRUVFVarvrl27dMEFFyglJUXz5s2T1Vr1WxakpaVJkpo1a1blbQEAAAAAOJ34zY38du3apfPPP18tW7bUE088of379ysjI0MZGRlefZKSkrR69WpJ0s8//6zp06dr7dq12r59u9577z2NGDFCf/rTn9SpUydfnQoAAAAAADXitJ/pr6xly5Zp69at2rp1q1q0aOG1zhgjSSoqKlJ6errn7vx2u12ffPKJnnzySeXn5ys+Pl6DBw/W/fffX+f1AwAAAABQ0yymNBGj2nJychQeHq7s7Gw5nU5fl1MpCZM/8Hy9feYgH1YCAAAAAKiqyuZQv7m8HwAAAAAAeCP0AwAAAADgpwj9AAAAAAD4KUI/AAAAAAB+itAPAAAAAICfIvQDAAAAAOCnCP0AAAAAAPgpQj8AAAAAAH6K0A8AAAAAgJ8i9AMAAAAA4KcI/QAAAAAA+ClCPwAAAAAAforQ30D9/aIzfV0CAAAAAKCWEfobqJZNQiVJvRKb+LgSAAAAAEBtIfQ3cAfzXb4uAQAAAABQSwj9DVRWQaEk6ae9eT6uBAAAAABQWwj9DdQv+/N9XQIAAAAAoJYR+gEAAAAA8FOEfgAAAAAA/BShv4GyWHxdAQAAAACgthH6GyiLSP0AAAAA4O8I/QAAAAAA+ClCfwPF5f0AAAAA4P8I/ZAxxtclAAAAAABqAaG/gTp2op/MDwAAAAD+idDfQB17eb+b1A8AAAAAfonQ30AVu/8I+kR+AAAAAPBPfhX6ExISZLFYvF4zZ86scJsjR47ojjvuUJMmTdSoUSMNHjxYe/furaOKfefttb95vmaiHwAAAAD8k1+Ffkl66KGHtGfPHs/rb3/7W4X9x40bp/fff18LFy7U559/rt27d+svf/lLHVXrO1d1be752jDXDwAAAAB+KcDXBdS0sLAwxcbGVqpvdna25s6dq9dff10XXnihJGnevHlq3769vv76a51zzjnlbudyueRyuTzLOTk5p154HTszNszzNTP9AAAAAOCf/G6mf+bMmWrSpIm6du2qxx9/XMXFxSfsu3btWhUVFal///6etqSkJLVs2VKpqakn3G7GjBkKDw/3vOLj42v0HOpCeHCgr0sAAAAAANQyv5rpv/POO3X22WercePGWrVqlaZMmaI9e/Zo1qxZ5fbPyMiQ3W5XRESEV3tMTIwyMjJOeJwpU6Zo/PjxnuWcnJx6F/zPbxft+Zq79wMAAACAfzrtQ//kyZP16KOPVthn06ZNSkpK8grinTp1kt1u1y233KIZM2bI4XDUWE0Oh6NG9+cLtmOe2bdpT65SWkX6sBoAAAAAQG047UP/hAkTNGrUqAr7JCYmltves2dPFRcXa/v27WrXrl2Z9bGxsSosLFRWVpbXbP/evXsrfV+A+uqYzK9Ne3II/QAAAADgh0770B8VFaWoqKhqbZuWliar1aro6Ohy16ekpCgwMFDLly/X4MGDJUnp6enauXOnevXqVe2a6xsu7gcAAAAA/3Tah/7KSk1N1TfffKMLLrhAYWFhSk1N1bhx4zR8+HBFRh6dxd61a5f69eun//znP+rRo4fCw8N14403avz48WrcuLGcTqf+9re/qVevXie8c7+/sB471c9n+gEAAADAL/lN6Hc4HFqwYIEeeOABuVwutW7dWuPGjfP6nH9RUZHS09NVUFDgafvXv/4lq9WqwYMHy+VyacCAAXr++ed9cQp16tjM7ybzAwAAAIBfshjDNO+pysnJUXh4uLKzs+V0On1dTqUUl7jV9r6PJEkPXNZBo/q09nFFAAAAAIDKqmwOtdZhTTiNWI6Z6memHwAAAAD8E6G/gTrm6n5u5AcAAAAAforQ30B538eP2A8AAAAA/ojQ30Ade3k/AAAAAMA/EfohNzP9AAAAAOCXCP0QmR8AAAAA/BOhH9zIDwAAAAD8FKEfzPQDAAAAgJ8i9IPP9AMAAACAnyL0AwAAAADgpwj9kGGmHwAAAAD8EqEfynOV+LoEAAAAAEAtIPRDb6391dclAAAAAABqAaEfOpBX6OsSAAAAAAC1gNAPAAAAAICfIvQDAAAAAOCnCP0AAAAAAPgpQj8AAAAAAH6K0A8AAAAAgJ8i9AMAAAAA4KcI/QAAAAAA+ClCPwAAAAAAforQDwAAAACAnyL0Q5I06+N0X5cAAAAAAKhhhH5Ikp7+dKuvSwAAAAAA1LBqhf78/PyargMAAAAAANSwaoX+mJgY3XDDDfryyy9ruh4AAAAAAFBDqhX6X3vtNWVmZurCCy/UmWeeqZkzZ2r37t01XVuVfPbZZ7JYLOW+vv322xNud/7555fpf+utt9Zh5QAAAAAA1I5qhf4rr7xS77zzjnbt2qVbb71Vr7/+ulq1aqVLL71UixYtUnFxcU3XeVK9e/fWnj17vF433XSTWrdurW7dulW47ZgxY7y2e+yxx+qoagAAAAAAas8p3cgvKipK48eP1w8//KBZs2bpk08+0dVXX624uDhNnTpVBQUFNVXnSdntdsXGxnpeTZo00bvvvqvRo0fLYrFUuG1ISIjXtk6ns8L+LpdLOTk5Xi8AAAAAAE43pxT69+7dq8cee0wdOnTQ5MmTdfXVV2v58uX65z//qUWLFunKK6+soTKr7r333tPBgwc1evTok/adP3++mjZtquTkZE2ZMuWkb1bMmDFD4eHhnld8fHxNlQ0AAAAAQI2xGGNMVTdatGiR5s2bp6VLl6pDhw666aabNHz4cEVERHj6/Pzzz2rfvr0KCwtrst5Ku+SSSyRJH374YYX95syZo1atWikuLk4//PCDJk2apB49emjRokUn3MblcsnlcnmWc3JyFB8fr+zs7JNeJXA6SZj8gdfy9pmDfFQJAAAAAKAqcnJyFB4eftIcGlCdnY8ePVrXXnutvvrqK3Xv3r3cPnFxcbrvvvuqs3svkydP1qOPPlphn02bNikpKcmz/Ntvv2np0qV68803T7r/m2++2fN1x44d1axZM/Xr108///yz2rRpU+42DodDDoejkmcAAAAAAIBvVCv079mzRyEhIRX2CQ4O1rRp06pV1LEmTJigUaNGVdgnMTHRa3nevHlq0qSJLr/88iofr2fPnpKkrVu3njD0AwAAAABQH1Qr9BcXF5d78zqLxSKHwyG73X7KhZWKiopSVFRUpfsbYzRv3jyNGDFCgYGBVT5eWlqaJKlZs2ZV3hYAAAAAgNNJtW7kFxERocjIyDKviIgIBQcHq1WrVpo2bZrcbndN13tSn376qbZt26abbrqpzLpdu3YpKSlJq1evlnT0vgPTp0/X2rVrtX37dr333nsaMWKE/vSnP6lTp051XToAAAAAADWqWjP9L7/8su677z6NGjVKPXr0kCStXr1ar7zyiu6//37t379fTzzxhBwOh+69994aLfhk5s6dq969e3t9xr9UUVGR0tPTPXfnt9vt+uSTT/Tkk08qPz9f8fHxGjx4sO6///46rRkAAAAAgNpQrbv39+vXT7fccouuueYar/Y333xTL774opYvX65XX31VDz/8sDZv3lxjxZ6uKnvXxNMNd+8HAAAAgPqpsjm0Wpf3r1q1Sl27di3T3rVrV6WmpkqSzj33XO3cubM6uwcAAAAAADWgWqE/Pj5ec+fOLdM+d+5cxcfHS5IOHjyoyMjIU6sOAAAAAABUW7U+0//EE09oyJAh+uijj9S9e3dJ0po1a7R582a99dZbkqRvv/1WQ4cOrblKAQAAAABAlVQr9F9++eVKT0/Xiy++qPT0dEnSxRdfrHfeeUcJCQmSpNtuu63GikTtCA8OVPbhIl+XAQAAAACoJVUO/UVFRRo4cKBmz56tGTNm1EZNqCMfj/uTej6y3NdlAAAAAABqSZU/0x8YGKgffvihNmpBHYtxBvm6BAAAAABALarWjfyGDx9e7o38AAAAAADA6aNan+kvLi7WSy+9pE8++UQpKSkKDQ31Wj9r1qwaKQ61Lyk2TJszcn1dBgAAAACgFlQr9G/YsEFnn322JOmnn37yWmexWE69KtSZZ//aVf1nfaHw4EBflwIAAAAAqGHVCv0rVqyo6TrgI6Vv0hhjfFwJAAAAAKCmVesz/aW2bt2qpUuX6vDhw5IIjvUR12UAAAAAgP+qVug/ePCg+vXrpzPPPFOXXHKJ9uzZI0m68cYbNWHChBotEHWDt2sAAAAAwP9UK/SPGzdOgYGB2rlzp0JCQjztQ4cO1ZIlS2qsONQ+zz0YSP0AAAAA4Heq9Zn+jz/+WEuXLlWLFi282s844wzt2LGjRgpD3eDyfgAAAADwX9Wa6c/Pz/ea4S+VmZkph8NxykWh7jHRDwAAAAD+p1qh/7zzztN//vMfz7LFYpHb7dZjjz2mCy64oMaKQ+3zXN3PTRgBAAAAwO9U6/L+xx57TP369dOaNWtUWFioe+65Rz/++KMyMzP11Vdf1XSNqEWW3y/wJ/IDAAAAgP+p1kx/cnKyfvrpJ5177rm64oorlJ+fr7/85S/6/vvv1aZNm5quEbXIwof6AQAAAMBvVWumX5LCw8N133331WQt8CGu7gcAAAAA/1Pt0J+VlaXVq1dr3759crvdXutGjBhxyoWhbhku8AcAAAAAv1Ot0P/+++9r2LBhysvLk9Pp/ONZ7zp6Uz9Cf/3B5f0AAAAA4L+q9Zn+CRMm6IYbblBeXp6ysrJ06NAhzyszM7Oma0Qd4PJ+AAAAAPA/1Qr9u3bt0p133qmQkJCargd1rPQqDTI/AAAAAPifaoX+AQMGaM2aNTVdC3zAc3U/qR8AAAAA/E61PtM/aNAgTZw4URs3blTHjh0VGBjotf7yyy+vkeJQ+/hMPwAAAAD4r2qF/jFjxkiSHnrooTLrLBaLSkpKTq0q1Dnu3g8AAAAA/qdaof/4R/Sh/rL8foE/N/IDAAAAAP9Tpc/0X3LJJcrOzvYsz5w5U1lZWZ7lgwcPqkOHDjVW3LEefvhh9e7dWyEhIYqIiCi3z86dOzVo0CCFhIQoOjpaEydOVHFxcYX7zczM1LBhw+R0OhUREaEbb7xReXl5tXAGpycu7wcAAAAA/1Wl0L906VK5XC7P8iOPPOL1iL7i4mKlp6fXXHXHKCws1JAhQ3TbbbeVu76kpESDBg1SYWGhVq1apVdeeUUvv/yypk6dWuF+hw0bph9//FHLli3T4sWL9cUXX+jmm2+ujVM4rTHRDwAAAAD+p0qX95vjrgE/frk2Pfjgg5Kkl19+udz1H3/8sTZu3KhPPvlEMTEx6tKli6ZPn65JkybpgQcekN1uL7PNpk2btGTJEn377bfq1q2bJOmZZ57RJZdcoieeeEJxcXHlHsvlcnm9+ZGTk3OKZ+c7pRP9dTmWAAAAAIC6Ua1H9p2OUlNT1bFjR8XExHjaBgwYoJycHP34448n3CYiIsIT+CWpf//+slqt+uabb054rBkzZig8PNzzio+Pr7kTqWu/p343mR8AAAAA/E6VQr/FYpHluA+BH7/sKxkZGV6BX5JnOSMj44TbREdHe7UFBASocePGJ9xGkqZMmaLs7GzP69dffz3F6n3Hoj/G77P0fT6sBAAAAABQ06p8ef+oUaPkcDgkSUeOHNGtt96q0NBQSfK65L0yJk+erEcffbTCPps2bVJSUlKV9lvbHA6H53vgTya/vV5f39vP12UAAAAAAGpIlUL/yJEjvZaHDx9eps+IESMqvb8JEyZo1KhRFfZJTEys1L5iY2O1evVqr7a9e/d61p1om337vGe3i4uLlZmZecJt/M2xF2pkHy7yXSEAAAAAgBpXpdA/b968Gj14VFSUoqKiamRfvXr10sMPP6x9+/Z5LtlftmyZnE7nCR8j2KtXL2VlZWnt2rVKSUmRJH366adyu93q2bNnjdR1ujv2wxmHi0p8VgcAAAAAoObVmxv57dy5U2lpadq5c6dKSkqUlpamtLQ05eXlSZIuuugidejQQddff73WrVunpUuX6v7779cdd9zhuRR/9erVSkpK0q5duyRJ7du318CBAzVmzBitXr1aX331lcaOHatrr732hHfuBwAAAACgvqjSTL8vTZ06Va+88opnuWvXrpKkFStW6Pzzz5fNZtPixYt12223qVevXgoNDdXIkSP10EMPebYpKChQenq6ior+uIx9/vz5Gjt2rPr16yer1arBgwfr6aefrrsT87HT5UaMAAAAAICaZzE8oP2U5eTkKDw8XNnZ2XI6nb4up0oO5Req6/RlnuVHB3fU0O4tfVgRAAAAAOBkKptD683l/agdx0/0T3p7vX7Zn+ebYgAAAAAANYrQ38C5y7nOY0/2kbovBAAAAABQ4wj9DVyx2+3rEgAAAAAAtYTQ38AVl3BLBwAAAADwV4T+Bi7GGVSmjVs7AgAAAIB/IPQ3cDYrj+wDAAAAAH9F6AcAAAAAwE8R+gEAAAAA8FOEfgAAAAAA/BShHwq08bl+AAAAAPBHhH7o0wnn+7oEAAAAAEAtIPRD8Y1DvJaNeGYfAAAAAPgDQj8AAAAAAH6K0A8AAAAAgJ8i9AMAAAAA4KcI/QAAAAAA+ClCPyRJvRKb+LoEAAAAAEANI/RDktSlZYSvSwAAAAAA1DBCPyRJTULtnq8NT+wDAAAAAL9A6Ick6fIucZ6vyfwAAAAA4B8I/ZAkBVr/+FFwM9UPAAAAAH6B0A9JktVi8Xz9zPItPqwEAAAAAFBTCP046o/Mr+92ZvmsDAAAAABAzSH0Q5J0zEQ/AAAAAMBPEPohyfvyfgAAAACAfyD0Q5LX1f2SpIN5Lp/UAQAAAACoOYR+SCp7eX9mfqFvCgEAAAAA1Jh6E/offvhh9e7dWyEhIYqIiCizft26dbruuusUHx+v4OBgtW/fXk899dRJ95uQkCCLxeL1mjlzZi2cwent+Mv7eWgfAAAAANR/Ab4uoLIKCws1ZMgQ9erVS3Pnzi2zfu3atYqOjtZrr72m+Ph4rVq1SjfffLNsNpvGjh1b4b4feughjRkzxrMcFhZW4/UDAAAAAFDX6k3of/DBByVJL7/8crnrb7jhBq/lxMREpaamatGiRScN/WFhYYqNja10LS6XSy7XH595z8nJqfS2p6vjL+9P/fmgzozhzQ8AAAAAqM/qzeX91ZGdna3GjRuftN/MmTPVpEkTde3aVY8//riKi4sr7D9jxgyFh4d7XvHx8TVVss9YjruV37T3fvRRJQAAAACAmlJvZvqratWqVXrjjTf0wQcfVNjvzjvv1Nlnn63GjRtr1apVmjJlivbs2aNZs2adcJspU6Zo/PjxnuWcnJx6H/x5Yh8AAAAA+B+fhv7Jkyfr0UcfrbDPpk2blJSUVKX9btiwQVdccYWmTZumiy66qMK+x4b3Tp06yW6365ZbbtGMGTPkcDjK3cbhcJxwXX1F5gcAAAAA/+PT0D9hwgSNGjWqwj6JiYlV2ufGjRvVr18/3Xzzzbr//vurXFPPnj1VXFys7du3q127dlXevr6yWYn9AAAAAOBvfBr6o6KiFBUVVWP7+/HHH3XhhRdq5MiRevjhh6u1j7S0NFmtVkVHR9dYXfWBhev7AQAAAMDv1JvP9O/cuVOZmZnauXOnSkpKlJaWJklq27atGjVqpA0bNujCCy/UgAEDNH78eGVkZEiSbDab542F1atXa8SIEVq+fLmaN2+u1NRUffPNN7rgggsUFham1NRUjRs3TsOHD1dkZKSvThUAAAAAgBpRb0L/1KlT9corr3iWu3btKklasWKFzj//fL311lvav3+/XnvtNb322muefq1atdL27dslSQUFBUpPT1dRUZGko5/NX7BggR544AG5XC61bt1a48aN8/qcPwAAAAAA9ZXFGGN8XUR9l5OTo/DwcGVnZ8vpdPq6nGpLmOz9pINVky9UXESwj6oBAAAAAJxIZXOotQ5rQj3z6eZ9vi4BAAAAAHAKCP3weOSqjl7Lr6za7ptCAAAAAAA1gtAPj/POaOq1vGVfno8qAQAAAADUBEI/PMp7at/+XFfdFwIAAAAAqBGEfnhYykn92YcLfVAJAAAAAKAmEPrhYS1nph8AAAAAUH8R+uER6wzydQkAAAAAgBpE6IdHeZf3AwAAAADqL0I/KpTvKvF1CQAAAACAaiL0o0JXPPeVr0sAAAAAAFQToR9e+p4Z5esSAAAAAAA1hNAPLy9en+LrEgAAAAAANYTQDy9BgTZflwAAAAAAqCGEfpyUMcbXJQAAAAAAqoHQjzJC7N6z/dsPFvioEgAAAADAqSD0o4z5N/X0Wv5uxyEfVQIAAAAAOBWEfpTRtJHDa/m5z7b6qBIAAAAAwKkg9KMMi8XXFQAAAAAAagKhH2VYjkv9v+zP91ElAAAAAIBTQehHGY1D7L4uAQAAAABQAwj9KCP4uLv3AwAAAADqJ0I/yjXtsg5eyz/vz/NRJQAAAACA6iL0o1zNwoO9lvv983MfVQIAAAAAqC5CP07A+LoAAAAAAMApIvSjXFFhjjJtbjdvBAAAAABAfULoR7lSWjUu0/bWd7/5oBIAAAAAQHXVm9D/8MMPq3fv3goJCVFERES5fSwWS5nXggULKtxvZmamhg0bJqfTqYiICN14443Ky+OmdeW5560ffF0CAAAAAKAK6k3oLyws1JAhQ3TbbbdV2G/evHnas2eP53XllVdW2H/YsGH68ccftWzZMi1evFhffPGFbr755hqs3L8YwyX+AAAAAFBfBPi6gMp68MEHJUkvv/xyhf0iIiIUGxtbqX1u2rRJS5Ys0bfffqtu3bpJkp555hldcskleuKJJxQXF3dKNdd3CU1CtP1ggVfbmh2H1D2h7KX/AAAAAIDTT72Z6a+sO+64Q02bNlWPHj300ksvVTgznZqaqoiICE/gl6T+/fvLarXqm2++OeF2LpdLOTk5Xi9/tGx83zJtriK3DyoBAAAAAFRHvZnpr4yHHnpIF154oUJCQvTxxx/r9ttvV15enu68885y+2dkZCg6OtqrLSAgQI0bN1ZGRsYJjzNjxgzPlQf+LNBW9j2h/XlHfFAJAAAAAKA6fDrTP3ny5HJvvnfsa/PmzZXe3z/+8Q/16dNHXbt21aRJk3TPPffo8ccfr/G6p0yZouzsbM/r119/rfFjnC6+ubef1/K4N9apuITZfgAAAACoD3w60z9hwgSNGjWqwj6JiYnV3n/Pnj01ffp0uVwuORxlnzsfGxurffv2ebUVFxcrMzOzwvsCOByOcvfnjwKsljJt/0ndoRvObe2DagAAAAAAVeHT0B8VFaWoqKha239aWpoiIyNPGNB79eqlrKwsrV27VikpKZKkTz/9VG63Wz179qy1uuqTEnfZeyIs/mE3oR8AAAAA6oF685n+nTt3KjMzUzt37lRJSYnS0tIkSW3btlWjRo30/vvva+/evTrnnHMUFBSkZcuW6ZFHHtHf//53zz5Wr16tESNGaPny5WrevLnat2+vgQMHasyYMZo9e7aKioo0duxYXXvttQ3+zv2lmjYq+4bJdzuzdKSoREGBNh9UBAAAAACorHoT+qdOnapXXnnFs9y1a1dJ0ooVK3T++ecrMDBQzz33nMaNGydjjNq2batZs2ZpzJgxnm0KCgqUnp6uoqIiT9v8+fM1duxY9evXT1arVYMHD9bTTz9ddyd2mrOWc3m/JE1fvFEPX9WxjqsBAAAAAFSFxVT0TDtUSk5OjsLDw5WdnS2n0+nrcmrc+t+yddmzX5Zp3z5zkA+qAQAAAABUNof69O79qB86tgj3dQkAAAAAgGog9AMAAAAA4KcI/aiUq1Na+LoEAAAAAEAVEfpRKU8M6VymbV/OER9UAgAAAACoLEI/qi3nSLGvSwAAAAAAVIDQj0pzBnk/4bGgkNAPAAAAAKczQj8qbdWUfl7Llz/7lf617CcfVQMAAAAAOBlCPyqtkSOgTNtTy7f4oBIAAAAAQGUQ+nHKikvcvi4BAAAAAFAOQj9O2UtfbVNhMcEfAAAAAE43hH6cskc+3Kwz7/9IH67f4+tSAAAAAADHIPSjSp79a9cTrrt9/nd1WAkAAAAA4GQI/aiSdjFhvi4BAAAAAFBJhH5UyRkxYbowKdrXZQAAAAAAKoHQjyp7aVR3X5cAAAAAAKgEQj+q5eyWEb4uAQAAAABwEoR+VMsrN/Qotz27oKiOKwEAAAAAnAihH9USFhRYbvvU9zYo9eeDKnGbOq4IAAAAAHA8Qj+qbeKAdmXa3k3brev+/bXmfbXNBxUBAAAAAI5F6Ee13X5+mxOue2vtb3VYCQAAAACgPIR+VJvFYtHrN/Usd92WfXl1XA0AAAAA4HiEfpyS3m2bltvOZ/oBAAAAwPcI/ag1B/Ncvi4BAAAAABo0Qj9OWVhQQLntKf/vE42at5pZfwAAAADwEUI/atVn6fs16e0ffF0GAAAAADRIhH6csqev7Vrh+rfW/qZXVm2vm2IAAAAAAB4WYwzXXp+inJwchYeHKzs7W06n09fl+MSrX+/QP97ZUOn+kwYmqVl4kAJtVnVsHq6WTUJqsToAAAAA8C+VzaH1JvQ//PDD+uCDD5SWlia73a6srCyv9S+//LJGjx5d7rZ79+5VdHR0uesSEhK0Y8cOr7YZM2Zo8uTJla6N0H9UYbFbZ97/0Snto0/bJmoT1Ug/7c1VjDNIA8+KVZ8zmmrnwQIlNA1VI0f59w8AAAAAgIaksjm03iSowsJCDRkyRL169dLcuXPLrB86dKgGDhzo1TZq1CgdOXLkhIG/1EMPPaQxY8Z4lsPCwmqm6AbGHnDqnxb5autBfbX1oGf53bTdp7zP8iRGheqX/flebfGNg9UsPFhx4UF6J2234sKD1CHOqatT4vV/K39Ru9gwXdGluV77eof6d4jRn85oqi378hQd5tBba3/TtT1aKtRu0/e/ZqlDM6cCbVbtyz2ipNij/wDdbiOLRbJYLHK7jYykohK3jJGC7TZPHaX9jJGK3UZFJW6FVvLNDrfbyGq11Nj3CQAAAED9Vm9m+ku9/PLLuvvuu8vM9B9v//79at68uebOnavrr7/+hP0SEhJ099136+677652Tcz0/+HLLQd02/y1ahxq146DBb4uBz7UIjJYu7IOq7Z/wzQOtSszv1DNI4I1qFMzzfniF0lS84hghTps6tm6iV79eofnjZSxF7SVzWrRU8u3SJKaNnLIEWDV6D4J+n8fbFJyc6e6xkcq2G7TL/vzFBFi16Y9ObqiS5yKSoyWb9qr7q0bK6qRQ1FhDj376Vbd1f8MHS4s8bxRk+8qVnLzcK3csl8frt+j54elaOOeHCXFhmnZxr3asCtb57eLUvPIYAUF2NQiMkQWi7R1f57Ojo/Uut+y1KSRXdkFRXKVuFVU7FajoABFNXLIYpHiIoK1aU+uwoMDZbFIuUeKle8qltViUVxEkDZn5Cr3SLHOinMqKTZMe7KPKCjQpv25LuW5ihQdFiRXcYksFovyXcWKDQ9ScYmRI8CqYLtNOYeLZWTkDAqUzWpRoM0q6+9vWBljPP81Rioscctus6qgqETBgTZZLZLbSBYdXecqcivEYVOBq0SBAaX7sshmLbsvq/XoG2IH8wvVONQu2+9vYJX8/uaXI8Ba5thBgX+8YXZ8v9MNb8oBAICa5HeX95eqbOj/5z//qenTp2vPnj0KDg4+Yb+EhAQdOXJERUVFatmypf76179q3LhxCgg48cyqy+WSy/XHM+hzcnIUHx9P6D/O3xeu01trf5MkdWsVqcahdn28ca+PqwIAABVpFxOm9L25Nba/5OZObdiVU2P7qw3tmzm1aU+OQuw2FRSWeK0LtB19o/JIkVvS0Ssb20Y10sY9OZ7lLvERWr0tUy0ig/XbocOebcODA5XSKlKFxW59ufWAWjYOUef4CB0uLNEnm7z/JnIEWOUqdqtNVKiyCop0ML9QwYE2NQ61a1fW0X3arBbFOoNUWOLW/lyX1/bRYQ7ty3UpKNCqI0Vuhdpt6hwfoVU/H1RiVKjsNquuTmmhg/mFKnAVa9OeXO3NPaLsw0XKKihSx+bhWr8rW2dEN9K5ZzTVvK+2S5IiQgIVaLMqsWmovtmWqR4JjbV6e6ako49t7pHQWIM6NdN3Ow9p855cJTcP14+7s+UMCtTyzfvUJT5Cab9mSTr6Rvs13VooMsSud9J2KaugSO1iw9SycYh2HMzXGTFh+u1Qgb7fmaXh57RSZn6hIkMC9cTHP6l101AdLizRBUnRat00RK4it3ZnH9FZcU65jVF6Rq6CA2366ueD2rQnRzed21pb9+epoLBEZ8U5FR8Zoi37crXq54OyWS2ySBrZO0G7s44o90iROsQ59W7abgUF2nRJcqzW78pWy8Yh2plZoLCgQLWIDNbyTXt1ccdm+m7HIcU4g/Tj7hx1T4iUJOUXlmjznhwN6tRMW/flKS4iWCF2m8KDA/XJpr3amXlYe7IO6/LOcdq8N1f7co6oV2IT9WjdRIE2i77ZlqmIkEAdyCuUq7hEHZo55QwO1K+ZBZr/9U5FOx26oF20dmYWqEOcU62bhmrHwQLFOB06UuSWMUb2AKtWbN6ncxKbaPnmfWrkCFBYUIBnAqawxC2LpJwjRbqkYzM1cgTISNp+IF+/Zh5Wl5YRyjtSrGK3WzmHi2SzWhUXESSrxaJ1v2YpMaqRmkUEye02mvvlNiXFOpUYFaqmjRzKPlyofFeJwoIC1DTMoQJXiX49VKBYZ5ByjhTJEWDVLwfyFR8ZosahRydUmjZy6EhRiWxWi1o2DlGLxiH6dlumNuzKVnLzcG3ck6PebZpo3a/Z6tIyQlkFhfpuxyEF/f7von0zpyJCAvX1LwcVHhwoR4BNiVGhkqSsgiLZrBYdyHMpM79QNqtFzqBAJTcPlzFHJxh2HMyXq9it886I0rfbM7U767CS48IV6ghQ84jgenHPsQYf+jt06KDzzz9fzz//fIX9Zs2apbPPPluNGzfWqlWrNGXKFI0ePVqzZs064TYPPPCAHnzwwTLthP6TM8bIbeSZwTu23WKxqMRtdKigUE0bOSQdvfz9l/35OjOmkYpKjHKOFKlpI4d+2Z+nVT8fVLeESDmDApV9uEiuYrfW78rWz/vy1D2hsRKahmhP1hF9/ctBbT+Yr5wjxWrZOET7c136ZttBnRUXrrU7DunWvm2Ume9Si8gQrdyyX99uPyTp6P/ki0rq1T8PAAAAADVgwc3n6JzEJr4uo0L1IvRPnjxZjz76aIV9Nm3apKSkJM9yZUJ/amqqevfurTVr1iglJaVKNb300ku65ZZblJeXJ4fDUW4fZvpxOjjRpcKlb6CUfl1QWOJ1T4Dj15e+2WKzWlRc4lbukWI1CgpQYbFbATaLHAE2GWP026HDah4RLKvVol1Zh9XIHqDAAIuyDxfJGCnQdvTScJvFoiNFJco9Uqzvfz2kqEYOdY6PUM6RIkU1cshmtchtpF2HDissKEDZh4t0pLhEdptVMc4glRijVVsPqJEjUGe3itAv+/PVqkmI9ua45Pj9vhGf/bRfknRWnFPvr9utcxKbyG6z6q3vftM13eIV6wzSjoP5WrvzkOIjQxRgtahZRLDSM3L0xU8H1Da6kYpK3Dq/XbSyDxdpx8F8Hchz6Zpu8dqyN0+HCgr13Iqt6tc+Rq7iEqX+fFDnnRGlsKAA5buK9U7absU6g5SRc0RRYQ7FRx69H8TKLft1cXIzfbn1gGdWJqFJiFzFbvVo3VglbqPFP+xR66ahyncVK9Bm9fTr2jJCLRuHlHsfi5vOba3XvtnhmWU63oVJ0fp08z5JUsfm4eoSH6FXv/7jBqWhdpt6tWlaZlbpeDbr0Z8FAACAhm5c/zN1V/8zfF1GhepF6N+/f78OHjxYYZ/ExETZ7XbPcmVC/4033qjvvvtO33//fZVr+vHHH5WcnKzNmzerXbt2ldqGz/QDAIDjHfsma3nLFfU91rE3gq3ssUrbJHldYXfsG8bHb1Nc4i5zJV6p0vtpHH+1Xukxjr/nR+kbzqVvJLqKS+QI+OO+H6VKd2WMvM7x2D9P3Uae+4oce9xcV7HsNqscAVZPn8NFJSpxG1ktFk97gNWiw0UlCrHbVOI2chW7FfL7DXQLS9yeN75L3EZBATblFxYr1H70zfIi99E3WwOsVhUWuxUUaNXh3y9HDrBaPfcRcRup2O1Wvqvk90umjew2qw7mF8pmsSjUESC3OVpXnqtYYUEB2n4gX7G/P764sMStkECb52MEhSVu5f5+dWNWQZGCA23KdRUpIsQuV1GJwoMDVWKMHAE25bmKZZGUmV+oaKdD+3Jcig0PkqvYLbcxRy+DzzqsqDCHGgUF6EhhiYLtNh3KL1J4cKCK3G4dLixRUKBNESGBchW7VVBY/PvPxNF7pUhSRIhduUeKFOYIlKu4RIE2q44UlyjfVazGoQ7lu4rlNkZ7c1zq1ipSua5ihdptysg5oqaNHMo5UiS7zaoDeS6F2AN0IM+lVo1DPfd7sVks2pyRq8IStyJDApV75Oj+woMDFRcRrOLfr/gsLHbrUEGh9ua4lNIqUrlHivTbocOKcQYpNjzo6H1fJBW4SuQ2RiVuo6378xRqD5AjwKrmkcH6ausB2awWBQXYFB4SqJaNQ5RVUKQAm0WNHAHacfDoZemhDpv257lktVi0O+uwOjRzKn1vrgoKj17GHmoPkCPQqmbhwVq7I1Mdm0dox8F8FRSWqG10I+3JPqwfd+forLhwZRUUKs9VLGdwoOIjg5VVUKSiEiNncIAiQ47en+hQQaHaxYbpYN7RS8/zXSVqHGpXVJhDQYE2fbs9U+1iw5RdUPT7JfM2hdhtOlJ09Fx/O3RY0c4gxYQ5FGy3aeu+PDmDAvXboQJt3JOjLvGRcgYfrTuhaah++C1LjgCr58rWoECbYp1B+uVAnmxWi1xFbrVqEqIvthxQYbFb57eLUmHx0d8Tea5iZR8uUqDNorwjxYp2BinvSLHW78pWl/gIBQVaFWA9+u8lPSNXTRrZ1Tk+QqH2AO3LPaLw4EAdKSqdYLJq855c7TiYr5jwIO04WKBWTULUyBEgu82qvN8/jtI4NFDRziAlxYbp5/152rwnVx1bhCvWGaT1u7K1M7NAkSF2RYba9cv+PJ3dMlJFv9//JyjQqpzDxdqf61KJMUpsGiqLxaKDeS7999tf1SMhUq5itzbuztGaHUev+n3kqo76a8+W5f5OPF3Ui9BfHScL/Xl5eWrWrJlmzJihsWPHVnn/8+fP14gRI3TgwAFFRkZWahtCPwAAAADUf7fPX6sP12fooSvO0oheCb4up0J+98i+nTt3KjMzUzt37lRJSYnS0tIkSW3btlWjRo08/d544w0VFxdr+PDhZfaxevVqjRgxQsuXL1fz5s2Vmpqqb775RhdccIHCwsKUmpqqcePGafjw4ZUO/AAAAAAA/9A2OkzdE1yee4z5g3oT+qdOnapXXnnFs9y1a1dJ0ooVK3T++ed72ufOnau//OUvioiIKLOPgoICpaenq6ioSJLkcDi0YMECPfDAA3K5XGrdurXGjRun8ePH1+q5AAAAAABOP+P/fKb05zN9XUaNqneX95+OuLwfAAAAAFCXKptDrXVYEwAAAAAAqEOEfgAAAAAA/BShHwAAAAAAP0XoBwAAAADATxH6AQAAAADwU4R+AAAAAAD8FKEfAAAAAAA/RegHAAAAAMBPEfoBAAAAAPBThH4AAAAAAPxUgK8L8AfGGElSTk6OjysBAAAAADQEpfmzNI+eCKG/BuTm5kqS4uPjfVwJAAAAAKAhyc3NVXh4+AnXW8zJ3hbASbndbu3evVthYWGyWCy+LueEcnJyFB8fr19//VVOp9PX5aAcjFH9wDid/hij0x9jVD8wTqc/xuj0xxjVD/VxnIwxys3NVVxcnKzWE39yn5n+GmC1WtWiRQtfl1FpTqez3vwgN1SMUf3AOJ3+GKPTH2NUPzBOpz/G6PTHGNUP9W2cKprhL8WN/AAAAAAA8FOEfgAAAAAA/BShvwFxOByaNm2aHA6Hr0vBCTBG9QPjdPpjjE5/jFH9wDid/hij0x9jVD/48zhxIz8AAAAAAPwUM/0AAAAAAPgpQj8AAAAAAH6K0A8AAAAAgJ8i9AMAAAAA4KcI/Q3Ec889p4SEBAUFBalnz55avXq1r0vyWzNmzFD37t0VFham6OhoXXnllUpPT/fqc+TIEd1xxx1q0qSJGjVqpMGDB2vv3r1efXbu3KlBgwYpJCRE0dHRmjhxooqLi736fPbZZzr77LPlcDjUtm1bvfzyy7V9en5p5syZslgsuvvuuz1tjJHv7dq1S8OHD1eTJk0UHBysjh07as2aNZ71xhhNnTpVzZo1U3BwsPr3768tW7Z47SMzM1PDhg2T0+lURESEbrzxRuXl5Xn1+eGHH3TeeecpKChI8fHxeuyxx+rk/PxBSUmJ/vGPf6h169YKDg5WmzZtNH36dB17j2DGqW598cUXuuyyyxQXFyeLxaJ33nnHa31djsfChQuVlJSkoKAgdezYUR9++GGNn299VdE4FRUVadKkSerYsaNCQ0MVFxenESNGaPfu3V77YJxq18n+LR3r1ltvlcVi0ZNPPunVzhjVrsqM0aZNm3T55ZcrPDxcoaGh6t69u3bu3OlZ32D+3jPwewsWLDB2u9289NJL5scffzRjxowxERERZu/evb4uzS8NGDDAzJs3z2zYsMGkpaWZSy65xLRs2dLk5eV5+tx6660mPj7eLF++3KxZs8acc845pnfv3p71xcXFJjk52fTv3998//335sMPPzRNmzY1U6ZM8fT55ZdfTEhIiBk/frzZuHGjeeaZZ4zNZjNLliyp0/Ot71avXm0SEhJMp06dzF133eVpZ4x8KzMz07Rq1cqMGjXKfPPNN+aXX34xS5cuNVu3bvX0mTlzpgkPDzfvvPOOWbdunbn88stN69atzeHDhz19Bg4caDp37my+/vprs3LlStO2bVtz3XXXedZnZ2ebmJgYM2zYMLNhwwbz3//+1wQHB5sXX3yxTs+3vnr44YdNkyZNzOLFi822bdvMwoULTaNGjcxTTz3l6cM41a0PP/zQ3HfffWbRokVGkvnf//7ntb6uxuOrr74yNpvNPPbYY2bjxo3m/vvvN4GBgWb9+vW1/j2oDyoap6ysLNO/f3/zxhtvmM2bN5vU1FTTo0cPk5KS4rUPxql2nezfUqlFixaZzp07m7i4OPOvf/3Lax1jVLtONkZbt241jRs3NhMnTjTfffed2bp1q3n33Xe9MlBD+XuP0N8A9OjRw9xxxx2e5ZKSEhMXF2dmzJjhw6oajn379hlJ5vPPPzfGHP2feWBgoFm4cKGnz6ZNm4wkk5qaaow5+kvMarWajIwMT58XXnjBOJ1O43K5jDHG3HPPPeass87yOtbQoUPNgAEDavuU/EZubq4544wzzLJly0zfvn09oZ8x8r1JkyaZc88994Tr3W63iY2NNY8//rinLSsryzgcDvPf//7XGGPMxo0bjSTz7bffevp89NFHxmKxmF27dhljjHn++edNZGSkZ8xKj92uXbuaPiW/NGjQIHPDDTd4tf3lL38xw4YNM8YwTr52/B/BdTke11xzjRk0aJBXPT179jS33HJLjZ6jP6goUJZavXq1kWR27NhhjGGc6tqJxui3334zzZs3Nxs2bDCtWrXyCv2MUd0qb4yGDh1qhg8ffsJtGtLfe1ze7+cKCwu1du1a9e/f39NmtVrVv39/paam+rCyhiM7O1uS1LhxY0nS2rVrVVRU5DUmSUlJatmypWdMUlNT1bFjR8XExHj6DBgwQDk5Ofrxxx89fY7dR2kfxrXy7rjjDg0aNKjM95Ex8r333ntP3bp105AhQxQdHa2uXbvq3//+t2f9tm3blJGR4fX9DQ8PV8+ePb3GKCIiQt26dfP06d+/v6xWq7755htPnz/96U+y2+2ePgMGDFB6eroOHTpU26dZ7/Xu3VvLly/XTz/9JElat26dvvzyS1188cWSGKfTTV2OB7//alZ2drYsFosiIiIkMU6nA7fbreuvv14TJ07UWWedVWY9Y+RbbrdbH3zwgc4880wNGDBA0dHR6tmzp9dHABrS33uEfj934MABlZSUeP2gSlJMTIwyMjJ8VFXD4Xa7dffdd6tPnz5KTk6WJGVkZMhut3v+x13q2DHJyMgod8xK11XUJycnR4cPH66N0/ErCxYs0HfffacZM2aUWccY+d4vv/yiF154QWeccYaWLl2q2267TXfeeadeeeUVSX98jyv63ZaRkaHo6Giv9QEBAWrcuHGVxhEnNnnyZF177bVKSkpSYGCgunbtqrvvvlvDhg2TxDidbupyPE7Uh/GquiNHjmjSpEm67rrr5HQ6JTFOp4NHH31UAQEBuvPOO8tdzxj51r59+5SXl6eZM2dq4MCB+vjjj3XVVVfpL3/5iz7//HNJDevvvQBfFwD4szvuuEMbNmzQl19+6etScIxff/1Vd911l5YtW6agoCBfl4NyuN1udevWTY888ogkqWvXrtqwYYNmz56tkSNH+rg6lHrzzTc1f/58vf766zrrrLOUlpamu+++W3FxcYwTUAOKiop0zTXXyBijF154wdfl4Hdr167VU089pe+++04Wi8XX5aAcbrdbknTFFVdo3LhxkqQuXbpo1apVmj17tvr27evL8uocM/1+rmnTprLZbGXuQrl3717Fxsb6qKqGYezYsVq8eLFWrFihFi1aeNpjY2NVWFiorKwsr/7HjklsbGy5Y1a6rqI+TqdTwcHBNX06fmXt2rXat2+fzj77bAUEBCggIECff/65nn76aQUEBCgmJoYx8rFmzZqpQ4cOXm3t27f33HG39Htc0e+22NhY7du3z2t9cXGxMjMzqzSOOLGJEyd6Zvs7duyo66+/XuPGjfNcQcM4nV7qcjxO1IfxqrzSwL9jxw4tW7bMM8svMU6+tnLlSu3bt08tW7b0/B2xY8cOTZgwQQkJCZIYI19r2rSpAgICTvq3REP5e4/Q7+fsdrtSUlK0fPlyT5vb7dby5cvVq1cvH1bmv4wxGjt2rP73v//p008/VevWrb3Wp6SkKDAw0GtM0tPTtXPnTs+Y9OrVS+vXr/f6n0Xp//BLf3n16tXLax+lfRjXk+vXr5/Wr1+vtLQ0z6tbt24aNmyY52vGyLf69OlT5lGXP/30k1q1aiVJat26tWJjY72+vzk5Ofrmm2+8xigrK0tr16719Pn000/ldrvVs2dPT58vvvhCRUVFnj7Lli1Tu3btFBkZWWvn5y8KCgpktXr/KWGz2TwzLIzT6aUux4Pff6emNPBv2bJFn3zyiZo0aeK1nnHyreuvv14//PCD198RcXFxmjhxopYuXSqJMfI1u92u7t27V/i3RIP6m9zXdxJE7VuwYIFxOBzm5ZdfNhs3bjQ333yziYiI8LoLJWrObbfdZsLDw81nn31m9uzZ43kVFBR4+tx6662mZcuW5tNPPzVr1qwxvXr1Mr169fKsL308yEUXXWTS0tLMkiVLTFRUVLmPB5k4caLZtGmTee655067x4PUJ8fevd8YxsjXVq9ebQICAszDDz9stmzZYubPn29CQkLMa6+95ukzc+ZMExERYd59913zww8/mCuuuKLcR4917drVfPPNN+bLL780Z5xxhtfjkrKyskxMTIy5/vrrzYYNG8yCBQtMSEgIj4KrpJEjR5rmzZt7Htm3aNEi07RpU3PPPfd4+jBOdSs3N9d8//335vvvvzeSzKxZs8z333/vuet7XY3HV199ZQICAswTTzxhNm3aZKZNm8Zjxo5R0TgVFhaayy+/3LRo0cKkpaV5/S1x7F3eGafadbJ/S8c7/u79xjBGte1kY7Ro0SITGBho5syZY7Zs2eJ5lN7KlSs9+2gof+8R+huIZ555xrRs2dLY7XbTo0cP8/XXX/u6JL8lqdzXvHnzPH0OHz5sbr/9dhMZGWlCQkLMVVddZfbs2eO1n+3bt5uLL77YBAcHm6ZNm5oJEyaYoqIirz4rVqwwXbp0MXa73SQmJnodA1VzfOhnjHzv/fffN8nJycbhcJikpCQzZ84cr/Vut9v84x//MDExMcbhcJh+/fqZ9PR0rz4HDx401113nWnUqJFxOp1m9OjRJjc316vPunXrzLnnnmscDodp3ry5mTlzZq2fm7/Iyckxd911l2nZsqUJCgoyiYmJ5r777vMKJoxT3VqxYkW5/w8aOXKkMaZux+PNN980Z555prHb7eass84yH3zwQa2dd31T0Tht27bthH9LrFixwrMPxql2nezf0vHKC/2MUe2qzBjNnTvXtG3b1gQFBZnOnTubd955x2sfDeXvPYsxxtTutQQAAAAAAMAX+Ew/AAAAAAB+itAPAAAAAICfIvQDAAAAAOCnCP0AAAAAAPgpQj8AAAAAAH6K0A8AAAAAgJ8i9AMAAAAA4KcI/QAAAAAA+ClCPwAAqHHbt2+XxWJRWlqar0sBAKBBI/QDANDAjBo1ShaLpcxr4MCBvi6tzn322WeyWCzKysrydSkAANSKAF8XAAAA6t7AgQM1b948rzaHw+GjagAAQG1hph8AgAbI4XAoNjbW6xUZGSlJ+utf/6qhQ4d69S8qKlLTpk31n//8R5K0ZMkSnXvuuYqIiFCTJk106aWX6ueff65SDS6XS5MmTVJ8fLwcDofatm2ruXPnetZ//vnn6tGjhxwOh5o1a6bJkyeruLjYsz4hIUFPPvmk1z67dOmiBx54wLNssVj0f//3f7rqqqsUEhKiM844Q++9956kox9BuOCCCyRJkZGRslgsGjVqVJXOAQCA0x2hHwAAeBk2bJjef/995eXledqWLl2qgoICXXXVVZKk/Px8jR8/XmvWrNHy5ctltVp11VVXye12V/o4I0aM0H//+189/fTT2rRpk1588UU1atRIkrRr1y5dcskl6t69u9atW6cXXnhBc+fO1f/7f/+vyufz4IMP6pprrtEPP/ygSy65RMOGDVNmZqbi4+P19ttvS5LS09O1Z88ePfXUU1XePwAApzMu7wcAoAFavHixJ2CXuvfee3XvvfdqwIABCg0N1f/+9z9df/31kqTXX39dl19+ucLCwiRJgwcP9tr2pZdeUlRUlDZu3Kjk5OSTHv+nn37Sm2++qWXLlql///6SpMTERM/6559/XvHx8Xr22WdlsViUlJSk3bt3a9KkSZo6daqs1srPW4waNUrXXXedJOmRRx7R008/rdWrV2vgwIFq3LixJCk6OloRERGV3icAAPUFM/0AADRAF1xwgdLS0rxet956qyQpICBA11xzjebPny/p6Kz+u+++q2HDhnm237Jli6677jolJibK6XQqISFBkrRz585KHT8tLU02m019+/Ytd/2mTZvUq1cvWSwWT1ufPn2Ul5en3377rUrn2qlTJ8/XoaGhcjqd2rdvX5X2AQBAfcVMPwAADVBoaKjatm17wvXDhg1T3759tW/fPi1btkzBwcFed/e/7LLL1KpVK/373/9WXFyc3G63kpOTVVhYWKnjBwcHn/I5WK1WGWO82oqKisr0CwwM9Fq2WCxV+hgCAAD1GTP9AACgjN69eys+Pl5vvPGG5s+fryFDhnjC88GDB5Wenq77779f/fr1U/v27XXo0KEq7b9jx45yu936/PPPy13fvn17paameoX6r776SmFhYWrRooUkKSoqSnv27PGsz8nJ0bZt26pUh91ulySVlJRUaTsAAOoLQj8AAA2Qy+VSRkaG1+vAgQNeff76179q9uzZWrZsmdel/ZGRkWrSpInmzJmjrVu36tNPP9X48eOrdPyEhASNHDlSN9xwg9555x1t27ZNn332md58801J0u23365ff/1Vf/vb37R582a9++67mjZtmsaPH+/5PP+FF16oV199VStXrtT69es1cuRI2Wy2KtXRqlUrWSwWLV68WPv37/e6eSEAAP6A0A8AQAO0ZMkSNWvWzOt17rnnevUZNmyYNm7cqObNm6tPnz6edqvVqgULFmjt2rVKTk7WuHHj9Pjjj1e5hhdeeEFXX321br/9diUlJWnMmDHKz8+XJDVv3lwffvihVq9erc6dO+vWW2/VjTfeqPvvv9+z/ZQpU9S3b19deumlGjRokK688kq1adOmSjU0b95cDz74oCZPnqyYmBiNHTu2yucBAMDpzGKO/zAcAAAAAADwC8z0AwAAAADgpwj9AAAAAAD4KUI/AAAAAAB+itAPAAAAAICfIvQDAAAAAOCnCP0AAAAAAPgpQj8AAAAAAH6K0A8AAAAAgJ8i9AMAAAAA4KcI/QAAAAAA+ClCPwAAAAAAfur/A6xxjbyYBCwSAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1200x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pylab\n",
    "\n",
    "pylab.rcParams[\"figure.figsize\"] = (12, 4)\n",
    "pylab.plot(counts, values)\n",
    "pylab.xlabel(\"Eval count\")\n",
    "pylab.ylabel(\"Energy\")\n",
    "pylab.title(\"Convergence with no noise\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "101ace68",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
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